Video: Writing Linear Equations in Standard Form

Video Transcript

Write the linear equation 𝑦 equals three 𝑥 plus four divided by 12 in standard form.

Standard form is 𝐴𝑥 plus 𝐵𝑦 equals 𝐶, where 𝐴, 𝐵, and 𝐶 are constants. They’re the numbers. So essentially, we want to get 𝑥 and 𝑦 on one side of the equation and then a number all by itself on the other side of the equation.

Our first step would be to multiply both sides of the equation by 12. They cancel on the right-hand side. And we have that 12𝑦 is equal to three 𝑥 plus four. So we need to get 𝑥 on the left-hand side of the equation to be with the 𝑦. And then the four will be left by itself on the right.

So let’s go ahead and subtract three 𝑥 from both sides of the equation. The three 𝑥s cancel on the right. And then on the left, negative three 𝑥 and 12𝑦 cannot be put together. They’re different variables. And in standard form, the variable 𝑥 is written first and then the variable 𝑦. So we end up with negative three 𝑥 plus 12𝑦 equals four. So our linear equation written in standard form will be negative three 𝑥 plus 12𝑦 equals four.